The contribution of the \(n=1\)  sector
was investigated in [1]}.
In this case the theory on the wrapped D3-brane is a
supersymmetric \(U(1)\)  gauge theory consisting of only neutral fields, and
we can easily calculate \({\cal I}_{(n_1,n_2,n_3)}\)  without any holonomy integrals.
It was found that
(REF ) reproduces the correct index
up to expected error due to multiple-wrapping contribution of order \(q^{2N+\delta _2}\)  with \(\delta _2=4\) .
